What are the approximate solutions of 4x² + 3 = -12x to the nearest hundredth?

Solution:

Given, the equation is 4x² + 3 = -12x

We have to find the approximate solutions to the equation.

Using quadratic formula,

\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

The equation can be written as 4x² + 12x + 3 = 0.

Here, a = 4, b = 12, c = 3

So, x =\(\frac{-12\pm \sqrt{(12)^{2}-4(4)(3)}}{2(4)}\\=\frac{-12\pm \sqrt{144-48}}{8}\\=\frac{-12\pm \sqrt{96}}{8}\\=\frac{-12\pm 9.8}{8}\)

Now, x = \(\frac{-12+9.8}{8}=\frac{-2.2}{8}=-0.275\)

x = \(\frac{-12-9.8}{8}=\frac{-21.8}{8}=-2.275\)

Therefore, the approximate solutions are -0.28 and -2.28.

What are the approximate solutions of 4x² + 3 = -12x to the nearest hundredth?

Summary:

The approximate solutions of 4x² + 3 = -12x to the nearest hundredth are -0.28 and -2.28.